On subalgebras of n× n matrices not satisfying identities of degree 2n-2

2003/05/29 by Daniel Birmajer, Birmajer, Daniel
Computer Science · Engineering · Mathematics · #15A24 #16R10 #Advanced Topics in Algebra #FOS: Mathematics #Matrix Theory and Algorithms #Rings and Algebras (math.RA) #graph theory and CDMA systems #math.RA #msc:15A24 #msc:16R10

paper · pdf · doi:10.48550/arxiv.math/0305430

11 pages

arxiv created 2003/05/29 · openalex publication_date 2003/05/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Amitsur-Levitski theorem asserts that M_n(F) satisfies a polynomial identity of degree 2n. (Here, F is a field and M_n(F) is the algebra of n × n matrices over F). It is easy to give examples of subalgebras of M_n(F) that do satisfy an identity of lower degree and subalgebras of M_n(F) that satisfy no polynomial identity of degree ≤ 2n-2. Our aim in this paper is to give a full classification of the subalgebras of n × n matrices that satisfy no nonzero polynomial of degree less than 2n.

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